## Determining L(2,1)-Span in Polynomial Space

### Konstanty Junosza-Szaniawski , Paweł Rzążewski

#### Abstract

A \$k\$-L(2,1)-labeling of a graph is a function from its vertex set into the set \$\\textbackslash\\0,...,k\\textbackslash\\\$, such that the labels assigned to adjacent vertices differ by at least 2, and labels assigned to vertices of distance 2 are different. It is known that finding the smallest \$k\$ admitting the existence of a \$k\$-L(2,1)-labeling of any given graph is NP-Complete. In this paper we present an algorithm for this problem, which works in time \$O(\\textbackslash\complexity \\textasciicircum\n)\$ and polynomial memory, where \$\\textbackslash\eps\$ is an arbitrarily small positive constant. This is the first exact algorithm for L(2,1)-labeling problem with time complexity \$O(c\\textasciicircum\n)\$ for some constant \$c\$ and polynomial space complexity.
 Author Journal series arXiv:1104.4506 Issue year 2011 Keywords in English 68R10, 05C15, 05C85, Computer Science - Data Structures and Algorithms, Computer Science - Discrete Mathematics, G.2.2, Mathematics - Combinatorics URL http://arxiv.org/abs/1104.4506 Language en angielski Score (nominal) 0 Citation count* 0 (2013-01-30)
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